Multicarrier receiver with channel estimator

ABSTRACT

Described is a transmission system for transmitting a multicarrier signal from a transmitter ( 10 ) to a receiver ( 20 ). The multicarrier signal comprises a plurality of subcarriers. The receiver ( 20 ) comprises a channel estimator ( 28 ) for estimating amplitudes of the subcarriers and for estimating time derivatives of the amplitudes. The receiver ( 20 ) further comprises an equalizer ( 24 ) for canceling intercarrier interference included in the received multicarrier signal in dependence on the estimated amplitudes and derivatives ( 29 ). The channel estimator ( 28 ) and/or the equalizer (24) are arranged for exploiting an amplitude correlation between the amplitudes of different subcarriers and/or for exploiting a derivative correlation between the derivatives of different subcarriers By making use of this correlation the complexity of the receiver ( 20 ) can be substantially reduced.

[0001] The invention relates to a transmission system for transmitting amulticarrier signal from a transmitter to a receiver.

[0002] The invention further relates to a receiver for receiving amulticarrier signal from a transmitter.

[0003] Multicarrier modulation methods, such as OFDM and MC-CDMA, havebeen around for some time now. OFDM or Orthogonal Frequency DivisionMultiplexing is a modulation method designed in the 1970's in whichmultiple user symbols are transmitted in parallel using differentsubcarriers. These subcarriers have overlapping (sinc-shaped) spectra,nonetheless the signal waveforms are orthogonal. Compared to modulationmethods such as BPSK, QPSK or MSK, OFDM transmits symbols which have arelatively long time duration, but a narrow bandwidth. Mostly, OFDMsystems are designed such that each subcarrier is small enough inbandwidth to experience frequency-flat fading. This also ensures thatthe subcarriers remain orthogonal when received over a (moderately)frequency selective but time-invariant channel. If the OFDM signal isreceived over a such channel, each subcarrier experiences a differentattenuation, but no dispersion.

[0004] The above mentioned properties of OFDM avoid the need for atapped delay line equalizer and have been a prime motivation to use OFDMmodulation methods in several standards, such as Digital AudioBroadcasting (DAB), the Digital Terrestrial Television Broadcast (DTTB)which is part of the Digital Video Broadcasting standard (DVB), and morerecently the wireless local area network standard HIPERLAN/2.Particularly in the DAB and DTTB applications, mobile reception underdisadvantageous channel conditions are foreseen, with both frequency andtime dispersion. Mobile reception of television has not been regarded asa major market up to now. Nonetheless, the DVB system promises to becomea high-speed delivery mechanism for mobile multimedia and internetservices. At the IFA '99 Consumer Electronics trade show, a consortiumof Nokia, Deutsche Telecom and ZDF demonstrated mobile web browsing,email access and television viewing over an OFDM DVB link, with a GSMreturn channel. With 8 k OFDM subcarriers, over the air DVB receptionfunctioned properly for vehicle speeds upto 50 mph. Mobile reception,i.e. reception over channels with Doppler spreads and the correspondingtime dispersion remains one of the problems associated with OFDM systemsin particular and multicarrier transmission systems in general. Whereasits robustness against frequency selectivity is seen as an advantage ofOFDM, the time-varying character of the channel is known to pose limitsto the system performance. Time variations are known to corrupt theorthogonality of the OFDM subcarrier waveforms. In such a case,Intercarrier Interference (ICI, also referred to as FFT leakage) occursbecause signal components from one subcarrier cause interference toother, mostly neighboring, subcarriers.

[0005] In the document “Equalization of FFT-leakage in mobile DVB-T”,Master Thesis in Radiocommunication from the Royal Institute ofTechnology, Stockholm, by Guillaume Geslin, April 1998, a multicarriertransmission system is disclosed. In this known transmission system ICIis cancelled (i.e. detected and removed from the received multicarriersignal) in the receiver by means of an equalizer. This equalizer derivesa vector of estimated symbols from a vector of received symbols. Theoperation of the equalizer is based upon a channel model in which theamplitudes of the subcarriers and die time derivatives thereof areindicative of the ICI. The receiver comprises a channel estimator whichgenerates estimates of these amplitudes and derivatives and suppliesthese estimates to the equalizer. The equalizer then cancels the ICI independence on the estimates of the amplitudes and derivatives. Thereceiver in the known transmission system is relatively complex, i.e. arelatively large number of computations is needed to implement thechannel estimator and the equalizer.

[0006] It is an object of the invention to provide a transmission systemaccording to the preamble in which the computational burden issubstantially reduced. This object is achieved in the transmissionsystem according to the invention, said transmission system beingarranged for transmitting a multicarrier signal from a transmitter to areceiver, the multicarrier signal comprising a plurality of subcarriers,the receiver comprising a channel estimator for estimating amplitudes ofthe subcarriers and for estimating time derivatives of the amplitudes,the receiver further comprising an equalizer for canceling intercarrierinterference included in the received multicarrier signal in dependenceon the estimated amplitudes and derivatives, wherein the channelestimator and/or the equalizer are arranged for exploiting an amplitudecorrelation between the amplitudes of different subcarriers and/or forexploiting a derivative correlation between the derivatives of differentsubcarriers. The invention is based upon the recognition that thecomplexity of the channel estimator and/or the equalizer can besubstantially reduced without seriously affecting the ICI cancellationprocedure by using correlation properties of the subcarriers. Althoughthe channel model is characterized by 2N parameters (with N being thenumber of subcarriers), the number of independent degrees of freedom issubstantially smaller in practice. This property comes from the factthat the propagation delay spread is often much smaller than the wordduration. This property also means that the entries in a vector ofestimated amplitudes are strongly correlated, so that the covariancematrix C_(a) of the amplitudes may be accurately approximated by alow-rank matrix. Similarly, the entries in a vector of derivatives arestrongly correlated and the covariance matrix C_(d) of the derivativesmay also be accurately approximated by a low-rank matrix. Using theselow-rank matrices in the channel estimator and/or equalizer results in asubstantial reduction of the complexity.

[0007] In an embodiment of the transmission system according to theinvention the receiver is a linear receiver and wherein the channelestimator comprises a reduced complexity filter for deriving vectors ofthe estimated amplitudes and derivatives from vectors of receivedsymbols and vectors of estimated symbols. The inventive concept may beadvantageously applied in linear receivers in which the estimatedsymbols are regarded as being a linear (data independent) combination ofthe received symbols and wherein the estimated symbols are derived fromthe received symbols by multiplying the received symbols with an inversematrix which depends on the estimated amplitudes and derivatives. Insuch a linear receiver the channel estimator may be implemented moreefficiently by means of a reduced complexity filter which exploits thecorrelation between the amplitudes and/or the derivatives.

[0008] In a further embodiment of the transmission system according tothe invention the receiver is a decision feedback receiver and whereinthe channel estimator comprises a smoothing filter for smoothing theestimated amplitudes and/or derivatives. Application of such a smoothingfilter has the advantage that it exploits the correlation amongderivatives. That is, since an estimate of a derivative on a particularsubcarrier is inaccurate because of noise or other effects, it is usefultake also into account the values of the derivative at neighboringsubcarriers. In practice this typically means that one smoothes thevalues of subcarriers of the various subcarriers.

[0009] In a further embodiment of the transmission system according tothe invention the receiver comprises a multiplication by N×N leakagematrix

, and wherein the multiplication is implemented as a sequence of anN-point IFFT, N pointwise multiplications and an N-point FFT. Anadditional complexity reduction is caused by the fact that the leakagematrix

is diagonalized by a Fourier basis, i.e. that

=FΔF^(H), where F is the N-point FFT matrix with normalized columns andΔ is a positive diagonal matrix. Hence, a multiplication by the N×Nmatrix

may be implemented as a sequence of an N-point IFFT, N pointwisemultiplications and an N-point FFT, thereby substantially reducingcomplexity.

[0010] In a further embodiment of the transmission system according tothe invention the decision feedback receiver comprises a decisionfeedback loop, and wherein the decision feedback loop comprises an errorcorrection decoder. By placing the error correction decoder within thedecision feedback loop the operation of the decision feedback receiveris improved. The ICI is cancelled on the basis of the estimated symbols27. By applying error correction decoding to these estimated symbols 27the ICI is cancelled on the basis of more reliable estimated symbols 27rendering an improved ICI cancellation.

[0011] The above object and features of the present invention will bemore apparent from the following description of the preferredembodiments with reference to the drawings, wherein:

[0012]FIG. 1 shows a block diagram of a transmission system according tothe invention,

[0013]FIGS. 2 and 3 and 5 and 6 show block diagrams of embodiments ofdecision feedback receivers according to the invention,

[0014]FIG. 4 shows some graphs illustrating the performance of thedecision feedback receiver as shown in FIG. 3.

[0015]FIG. 7 shows a block diagram of a MC-CDMA transmitter,

[0016]FIG. 8 shows a block diagram of an embodiment of a MC-CDMAdecision feedback receiver according to the invention.

[0017] In the Figures, identical parts are provided with the samereference numbers.

[0018] The invention is based upon the development of a simple andreliable channel representation In order to do so, we will consider amulticarrier transmission system, e.g. an OFDM or MC-CDMA transmissionsystem, with N subcarriers spaced by f_(s). Each subcarrier has arectangular envelope of a finite length that, including the cyclicextension, exceeds (1/f_(s)). Let s=[s₁ . . . s_(N)]^(T) be a vector ofN transmitted symbols, then the transmitted continuous time basebandsignal may be written as follows: $\begin{matrix}{{x(t)} = {\sum\limits_{k = 1}^{N}{s_{k}{{\exp \left( {\quad 2\quad \pi \quad f_{s}k\quad t} \right)}.}}}} & (1)\end{matrix}$

[0019] In the case of a frequency selective time-varying additive whiteGaussian noise (AWGN) channel, the received continuous time signal maybe written as follows: $\begin{matrix}{{{y(t)} = {{\sum\limits_{k = 1}^{N}{s_{k}{H_{k}(t)}{\exp \left( {\quad 2\quad \pi \quad f_{s}k\quad t} \right)}}} + {n(t)}}},} & (2)\end{matrix}$

[0020] wherein the coefficient H_(k)(t) represents the time-varyingfrequency response at the k-th subcarrier, for 1≦k≦N, and wherein n(t)is AGWN within the signal bandwidth. We assume that the channel slowlyvaries so that only a first order variation may be taken into accountwithin a single data block duration. In other words, we assume thatevery H_(k)(t) is accurately approximated by

H _(k)(t)≈H _(k)(t _(r))+H _(k) ^(′)(t _(r))(t−t _(r)),   (3)

[0021] wherein H_(k) ^(′)(t) is the first order derivative of H_(k)(t)and wherein t_(r) is a reference time within the received data block.Note that the time varying channel H_(k)(t) may also take into account aresidual frequency offset, after the coarse frequency synchronization.

[0022] The received baseband signal is sampled with a sampling offsett_(o) and a rate Nf_(s) and a block of its N subsequent samples[y(t_(o)), y(t_(o)+T), . . . , y(t_(o)+(N−1)T)] (with$T = \frac{1}{N\quad f_{s}}$

[0023] ) is subject to a fast fourier transform (FFT) of size N. Lety=[y₁, . . . , y_(N)]^(T) be the vector of N FFT samples so that$\begin{matrix}{y_{k} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{y\left( {t_{o} + {n\quad T}} \right)}{{\exp \left( {{- {2}}\quad \pi \quad k\quad {n/N}} \right)}.}}}}} & (4)\end{matrix}$

[0024] After substituting (2) into (4) and using the approximation (3),we obtain $\begin{matrix}{{y_{k} = {{a_{k}s_{k}} + {\sum\limits_{i = 0}^{N - 1}{d_{l}s_{l}{\sum\limits_{n = 0}^{N - 1}{\left( {n/N} \right){\exp \left( {{- }\quad 2\quad {\pi\left( \quad {k - l} \right)}\quad {n/N}} \right)}}}}} + n_{k}}},} & (5)\end{matrix}$

a _(l)=exp(i2πf _(s) lt ₀)(H _(l)(t _(r))+H _(l) ^(′)(t _(r)) (t ₀ −t_(r))),   (6)

d _(l)=exp(i2πf _(s) lt ₀)TH_(l) ^(′)(t_(r)),   (7)

[0025] wherein n_(k) for 1≦k≦N, are the samples of AWGN having a certainvariance a σ². It is convenient to rewrite the result (5) in a closematrix form. To this end, we define diagonal matrices A=diag{a_(l), . .. , a_(N)}, D=diag {d_(l), . . . , d_(N)} and an N×N matrix$\begin{matrix}{{\Xi = \left\{ \Xi_{p,q} \right\}_{p,{q = 1}}^{N}},{\Xi_{p,q} = {\sum\limits_{n = 0}^{N - 1}{\left( {n/N} \right){{\exp \left( {{- }\quad 2\quad {\pi\left( \quad {p - q} \right)}\quad {n/N}} \right)}.}}}}} & (8)\end{matrix}$

[0026] With this notation, the expression (5) is equivalent to

y=A s+

D s+n,   (9)

[0027] wherein n=[n_(l), . . . , n_(N)]^(T) is an N×1 vector of AWGN. Inthe channel model (9), the effect of the channel is represented by twosets of N parameters a=[a_(l), . . . , a_(N)]^(T) and d=[d_(l), . . . ,d_(N)]^(T). Check that H_(l)(t_(r))+H_(l)^(′)(t_(r))(t_(o)−t_(r))≈H_(l)(t_(o)), hence the coefficients a_(k), for1≦k≦N, are equal to the complex amplitudes of the channel frequencyresponse rotated by the sampling phase exp(i2πf_(s)lt₀). Similarly, thecoefficients d_(k), for 1≦k≦N are equal to the time-domain derivativesof the complex amplitudes of the channel frequency response scaled bythe sampling period T and rotated by the same sampling phaseexp(i2πf_(s)lt₀).

[0028] Note that an inter-carrier interference occurs when the channelresponse varies in time (i.e. d≠0). This interference is defined by thevector d as well as the fixed N×N matrix

. It can be is easily seen that according to (8) the latter matrix is aToeplitz Hermitian matrix and that${\Xi = \left\{ \Xi_{p,q} \right\}_{p,{q = 1}}^{N}},{\Xi_{p,q} = \left\{ \begin{matrix}{{\left( {N - 1} \right)/2},} & {{p = q};} \\{{- \left( {1 - ^{\quad 2\quad {{\pi {({q - p})}}/N}}} \right)^{- 1}},} & {p \neq {q.}}\end{matrix} \right.}$

[0029] Later in this document, we will call a the (vector of)amplitudes, d the (vector of) derivatives and

the leakage matrix. In the above expression, the values on the diagonalof

depend on the (arbitrary) choice of the reference time instant t₀, andcan therefor vary depending on the embodiment of receiver. Typicalchoices for t₀ are time beginning, the end or middle of a frame window.For t₀ chosen near the middle of the frame, the diagonal terms tend tobecome approximately zero.

[0030] For the implementation of a receiver based on the principlesdiscussed here, multiplication by

may be prohibitively complicated particularly for large N (manysubcarriers). One can of course only use the terms near the diagonal andexploit the Toeplitz character of

by implementing it as a delay-line filter. But there are more efficientimplementations of

. We note that the first-order ICI terms result from amplitudes linearlyincreasing with time. That is, one can implement

as the cascade of

[0031] 1. an I-FFT operation (to go back from a frequency domainrepresentation of the subcarriers to time domain),

[0032] 2. a multiplication of the resulting time-domain signal by adiagonal matrix, i.e., a weighting of each component by a scalar. In itsbasic form the weighting is by a linearly increasing function, but inpractice one may divert from this, for instance to jointly optimize thereduction of ICI and the avoidance of noise enhancements.

[0033] 3. an FFT operation to return to the frequency domainrepresentation in which subcarrier signals are typically processed.

[0034] This allows the implementation of

with a complexity NlogN, instead of N² multiplications. The inverse of

can be implemented with this structure. For the inverse the terms on thediagonal of the matrix of step 2 will approximately be of the form orn/(c+n²), where n is the index at the output number of the I-FFT. Wewill exploit this in several receiver embodiments to be given later. Ina practical implementation, it is useful to use the same hardwarecircuit for the FFT and IFFT used for

the hardware used for the main FFT operation to retrieve subcarriersignals.

[0035] To process the received signal, the set of channel parameters aand d should be estimated. The estimation accuracy of these 2N scalarparameters may be enhanced if the statistical properties of the channelare used. First of all, we assume that channel variations are slowenough so that H_(k) ^(′)(t) do not change substantially within theduration of a symbol. In this case, we may rewrite (6) and (7) asfollows:

a _(l)≈exp(i2πf _(s) lt _(o))H _(l)(t_(o)),

d _(l)≈exp(i2πf _(s) lt _(o))TH_(l) ^(′)(t _(o)), 1≦l≦N.   (10)

[0036] Let us analyze the relationship between the quantities a, d andphysical parameters of the propagation channel, namely the set of its Kpropagation delays {τ₀, . . . , τ_(k)}, the corresponding Doppler shifts(f₀, . . . , f_(K)}, and complex amplitudes {h₀, . . . , h_(K)}. Notethat the statistical properties of the channel frequency response dependon the relative delays and Doppler shifts whereas the group delay and/orDoppler shift result in rotations of h_(k), for 1≦k≦K, where therotations are taken care of by time and carriersynchronization/tracking. Hence, we may assume without loss ofgenerality that τ₀=0 and f₀=0. Now, the channel frequency response H_(l)and its derivative H_(l) ^(′)may be written as follows: $\begin{matrix}{{{H_{l}(t)} = {\sum\limits_{n = 0}^{k}{h_{n}{\exp \left( {\quad 2\quad {\pi \left( {{f_{n}t} - {f_{s}l\quad \tau_{n}}} \right)}} \right)}}}},{{H_{l}^{\prime}(t)} = {i\quad 2\quad \pi {\sum\limits_{n = 0}^{k}{f_{n}h_{n}{\exp \left( {{2}\quad {\pi \left( {{f_{n}t} - {f_{s}l\quad \tau_{n}}} \right)}} \right)}}}}},{1 \leq l \leq {N.}}} & (11)\end{matrix}$

[0037] The relationships (10) and (11) may be readily used to deduce thestatistical properties of the amplitudes a and derivatives d. Wheneverthe number of propagation paths is big enough (ideally K>>N ), the setof coefficients {H_(l)(t), H_(l) ^(′)(t)}_(1≦l≦N) may be consideredjointly Gaussian distributed. Moreover, one can show that the sets{H_(l)(t)}_(1≦l≦N) and {H_(l) ⁴⁰ (t)}_(1≦l≦N) are mutually uncorrelatedwhen {h_(k)}_(1≦k≦K) are uncorrelated and the Doppler spectrum has asymmetric shape. In this case, the vectors a and d may be assumedstatistically independent multivariate Gaussian with zero mean andcovariance matrices

E }aa ^(H) }=C _(a) , E{dd ^(H) }=C _(d)   (12)

[0038] where E{.} stands for the mathematical expectation operator andC_(a), C_(d) are N×N Hermitian non-negative definite matrices.

[0039] An important particular case of C_(a), C_(d) corresponds to astandard model for mobile channels, as described in the book MicrowaveMobile Communications by C. Jakes, John Wiley & Sons, Inc., 1974. Thismodel (known as Jakes model) assumes independent contributions ofdifferent propagation paths, an exponential delay profile and uniformlydistributed angles of incidence for different paths. One can show thatin this case, $\begin{matrix}{{C_{a} = C},{C_{d} = {\gamma^{2}C}},{\gamma^{2} = {\frac{1}{2}\left( {2\pi \quad f_{\Delta}T} \right)^{2}}},{C_{p\quad q} = \frac{1}{1 + {i\quad 2{\pi \left( {p - q} \right)}f_{s}T_{\Delta}}}},{1 \leq p},{q \leq N},} & (13)\end{matrix}$

[0040] wherein f_(Δ)is the magnitude of the Doppler spread and whereinT_(Δ)is the root mean square propagation delay spread. The last twoparameters depend on the mobile velocity and propagation environmentrespectively.

[0041] Although the outlined channel model is characterized by 2Nparameters, the number of independent degrees of freedom issubstantially smaller in practice. This property comes from the factthat the propagation delay spread is often much smaller than the wordduration. This property also means that the entries of a are stronglycorrelated, to the extend that the covariance matrix C_(a) may beaccurately approximated by a low-rank matrix. Similarly, the entries ofd are strongly correlated and the covariance matrix C_(d) may also beaccurately approximated by a low-rank matrix. Let us consider the Jakesmodel and therefore (13). Define the eigendecomposition of C:

C=UΛU^(H),   (14)

[0042] wherein U is the N×N unitary matrix of eigenvectors of C andwherein Λ is the N×N positive diagonal matrix of its eigenvalues {Λ_(l),. . . , Λ_(N)}. Assume that the eigenvalues are ordered so that sequenceof {Λ_(l), . . . , Λ_(N)} is non-increasing. Under Jakes model, theelements of this sequence have an exponentially decaying profile:

Λ_(k)˜exp(−f _(s) T _(Δ) k), for 1≦k≦N.   (15)

[0043] Hence, the sequence of eigenvalues may be accurately approximatedwith a relatively small number r of non-zero values:

{Λ_(l), . . . , Λ_(N)}≈{Λ_(l), . . . ,Λ_(r),0 . . . 0}.   (16)

[0044] The aforementioned properties of the channel parameters (i.e.amplitudes and derivatives) can be extensively used to derive reducedcomplexity procedures for channel equalization with ICI removal.Evidently, in situations where the statistical channel may divert fromthe idealized theoretical situation, theses models may still inspire thedesign of practical receiver. The mismatch between the actual channeland the idealized channel model may lead to a (small) performancepenalty. However, this does not mean that the receiver principlesdisclosed in this invention, can not be used successfully.

[0045]FIG. 1 shows a block diagram of a transmission system according tothe invention. The transmission system comprises a transmitter 10 and areceiver 20. The transmission system may comprise further transmitters10 and receivers 20. The transmitter 10 transmits a multicarrier signalvia a wireless channel to the receiver 20. The multicarrier signal maybe an OFDM signal or a MC-CDMA signal. The receiver 20 comprises ademodulator 22 for demodulating the received multicarrier signal, whichreceived multicarrier signal comprises vectors of received symbols. Thedemodulator 22 may be implemented by means of a FFT. The demodulatedmulticarrier signal is supplied by the demodulator 22 to an equalizer24. The equalizer 24 cancels intercarrier interference which may beincluded in the received multicarrier signal. The equalizer 24 outputsvectors of estimated symbols 25 (which have been derived from thevectors of received symbols) to a (soft) slicer 26. The slicer 26produces soft metrics (soft decisions) and/or binary estimates (harddecisions) of the (coded) bits to be used in the further signalprocessing parts of the receiver (which are not shown), e.g. a FECdecoder. The output signal of the slicer 26 may also be regarded ascomprising estimated symbols 27. The receiver 20 further comprises achannel estimator 28 for estimating amplitudes 29 of the subcarriers andfor estimating time derivatives 29 of the amplitudes. The equalizer 24cancels the intercarrier interference included in the receivedmulticarrier signal in dependence on the estimated amplitudes andderivatives 29 which are supplied by the channel estimator 28 to theequalizer 24. The channel estimator 28 may comprise a reduced complexityfilter for deriving vectors of the estimated amplitudes and derivatives29 from the vectors of received symbols 23 and vectors of estimatedsymbols 27.

[0046] We now continue with an example embodiment of a receiver based onthe developed channel model. If an OFDM receiver is extended such thatit can not only reliably estimate amplitudes â (as conventionalreceivers do), but also (complex valued, e.g. including phaseinformation) derivatives {circumflex over (d)} (which is not common fornormal OFDM receivers), then the user data can be recovered as follows:

[0047] create the matrix Q=â+

{circumflex over (d)}, with â and {circumflex over (d)} denoting theestimates of amplitudes and derivatives, respectively. Note that thereceiver receives the signal y=Qs+n (according to (9)).

[0048] Then estimate s as ŝ=Q′y. Such a receiver is called a linearreceiver. The receiver 20 as shown in FIG. 1 may be regarded as such alinear receiver when the equalizer 24 implements the matrixmultiplication Q′y. Here Q′ plays the role of an inverse of Q. At leasttwo approaches come to mind. In a zero-forcing approach, Q′ is thestrict algebraic inverse of Q. In an MMSE setting Q′ is chosen to ensurethat ŝ=Q′y=Es|y, i.e. the conditional expectation of s given y. Thistypically minimizes the mean square error ∥ŝ−s∥². in a zero-forcingreceiver, the ICI is effectively cancelled but noise is amplified. Thiscan lead to undesirable results. The MMSE receiver optimizes the jointstrength of noise and residual ICI. This receiver requires an adaptive(typically real-time) inversion of a matrix which depends on theinstantaneous channel characteristics â and {circumflex over (d)}.

[0049] It is also possible to use a so-called decision feedbackreceiver. The channel model presented earlier in this document revealsthat one can refine and improve this decision feedback receiver inseveral aspects, among them:

[0050] A feedback loop in which the estimates of the derivatives aremore accurate if one exploits more knowledge about the statisticalbehavior of these derivatives, in particular correlation.

[0051] A feedback loop in which the error correction code is used within the loop. As a side note we mention that for multi-carrier CDMA, thespreading code plays an identical role as the error correction code.That is, one can place the decoding (whether is occurs as CDMAdespreading, as error correction decoding, or any other form) within theloop.

[0052]FIG. 2 shows a block diagram of an embodiment of a decisionfeedback receiver. The decision feedback receiver 20 comprises ademodulator 22 for demodulating the received multicarrier signal, whichreceived multicarrier signal comprises vectors of received symbols. Thedemodulator 22 may be implemented by means of a FFT. The demodulatedmulticarrier signal is supplied by the demodulator 22 to a subtracter32. The subtracter 32 subtracts an estimation of the ICI included in thereceived multicarrier signal from the demodulated multicarrier signal.The resulting ‘ICI-free’ signal is supplied to an equalizer 24 fornormal equalization of the signal and to a channel estimator 28. Theequalizer 24 may also comprise a slicer. The equalizer 24 operates independence on estimated amplitudes which are supplied to the equalizer24 by the channel estimator 28. The output signal of the equalizer 24,comprising vectors of estimated symbols, is supplied to a multiplier 31.Furthermore, the output signal of the equalizer 24 is also supplied tofurther signal processing parts of the receiver (which are not shown).The channel estimator 28 estimates the amplitudes and time-derivativesof the subcarriers. The estimated amplitudes 29 are supplied to theequalizer 24 and the estimated derivatives 29 are supplied to themultiplier 31. The multiplier 31 multiplies the estimated derivativesand the estimated data symbols and supplies the resulting signal to afilter 30 which implements the leakage matrix . The filtered signalwhich is an estimate of the ICI is then supplied to the subtracter 32.

[0053] Based on this general scheme another decision feedback receivercan be devised as illustrated in FIG. 3. Here, the FFT demodulator isnot shown (but is thought to be present). The signal path comprising Y₀,Y₁, Y₂, the slicer 26, the forward error control decoding 42 and thechannel estimation (whether blind or pilot based) are similar to thedesign of a conventional, state-of-the-art OFDM receiver. In thereceiver described here, we introduced a subtraction of the estimatedICI (

Z₅), using Y₁=Y₀-

Z₅. Here Z₅ is an estimation of the modulated derivatives {circumflexover (d)} s. The signal path Z₁, Z₂, Z₃, Z₄ estimates the derivatives ofthe amplitudes, with Z₄={circumflex over (d)}. The rationale behind thecircuit is that Z₁ recovers the ICI, because an estimate of themodulated subcarriers is subtracted from Y₀. Only noise, ICI and anestimation error remain. Filter 50 is used to estimate the modulatedderivatives from the ICI. It inverts the leakage matrix

, though not necessarily as the inverse in strict mathematical sense.Preferable this is done while avoiding excessive noise enhancement orenhancement of estimation error. Modulation of the derivatives isremoved in the step Z₂→Z₃. Filter 54 exploits the correlation betweenthe subcarrier derivatives, to generate a better estimate Z₄. A usefulimplementation of

involves the cascaded use of an (Inverse) FFT, a multiplication (with adiagonal matrix) and an FFT.

[0054] Although the circuit is depicted as hardware building blocks, atypical implementation may involve iterative software processing. Weexperimented with an iteration method comprised of the following stepsfor iteration round i:

[0055] Input: observation Y₀, as well as the (i−1)-th estimate ofamplitudes â(i−1), derivatives {circumflex over (d)}(i−1), and dataŝ(i−1). Here values between brackets denote the number of the iterationround.

[0056] Calculation of Y₁(i), using previous estimates of derivatives{circumflex over (d)}(i−1) and data ŝ(i−1), using Y₁(i)=Y−

({circumflex over (d)}(i−1)ŝ(i−1))

[0057] New estimate amplitudes â(i) from Y₁(i), and (not depicted)possibly exploiting knowledge of amplitudes and derivatives in theprevious frame.

[0058] New estimate of data ŝ(i)

[0059] Calculation of Z₁(i), Z₂(i), Z₃(i), Z₄(i), Z₅(i),

[0060] (Optional step, not depicted in the Figure) possible use ofknowledge of amplitudes and derivatives in the previous frame. This stepinvolves operations which exploit correlation among subcarrierderivatives.

[0061] Output: new estimate of amplitudes â(i), derivatives {circumflexover (d)}(i), and data ŝ(i)

[0062] Starting condition is the all-zero vector for â(0), {circumflexover (d)}(0) and ŝ(0).

[0063] The filter 50 attempts to recover an estimate of d s from Z₁ byfiltering Z_(2=M) ₁Z₁. One mathematical approach is to use theorthogonality principle for an MMSE estimate. In this case, anappropriate choice for M₁ follows from the requirement E[(Z₂−ds) Z₁^(H)]=0_(N)

[0064] We define e as the vector of decision errors, withe=as−{circumflex over (a s)}. This gives M₁={E[ds(ds)^(H)]

^(H)+E[dse^(H)]} [E[

ds(ds)^(H)

^(H)+I_(N)σ_(n) ²+ee^(H)+

dse^(H)+(ds)^(H)

^(H)e]]⁻¹, wherein σ_(n) is the variance of the noise. Modeling and(pre-)calculating some of the statistical expectation values here can bedone, but may not be practical for receiver designers. So next we willsearch for simplifying approximations.

[0065] One can simplify the resulting M₁ as M₁=

^(H)[

^(H)+G]⁻¹, wherein G is empirically determined as G=c_(l)I_(N) with aconstant c_(l) which may be adapted to specific propagationenvironments, for instance the average BER, the average SNR or the speedof the mobile receiver.

[0066] Z₃ approximates {circumflex over (d)}, however it contains errorcontributions due to AWGN and estimation error in {circumflex over (d)}and ŝ. Here we can exploit statistical knowledge that we have developedabout the channel behavior, e.g. on correlation of derivatives. Thecircuit from Z₂, multiplication by 1/x, Z₃, M₂, Z₄ to multiplier Z₅ isintended to perform this task. The multiplications aim at removing andreinserting the data modulated onto the signal. A smoothing operation M₂occurs in between. An MMSE filter to estimate Z₄ as closelyapproximating {circumflex over (d)} follows from the orthogonalityprinciple E(Z₄−{circumflex over (d)}) Z₃ ^(H)=0_(N), thusM₂=E{circumflex over (d)}Z₃ ^(H)[EZ₃Z₃ ^(H)]⁻¹. In practice one may findit acceptable to crudely approximate M₂=E{circumflex over (dd)}^(H)[E{circumflex over (d d)}^(H)+R₃]⁻¹. Experiments revealed thatR_(3=c) ₂I_(N) with a constant c₂ is a workable solution.

[0067]FIG. 4 shows some graphs illustrating the performance of thedecision feedback receiver as shown in FIG. 3. The strength of theamplitudes and the derivatives (in dB) is plotted against the subcarriernumber. Graph 60 shows the strength of the actual amplitudes, whilegraph 62 shows the strength of the estimated amplitudes. Graph 64 showsthe strength of the actual derivatives, while graph 66 shows thestrength of the estimated derivatives. It can be seen that theamplitudes are estimated very well by the decision feedback receiver ofFIG. 3, while the estimated derivatives deviate somewhat from the actualderivatives.

[0068]FIG. 5 shows another decision feedback receiver based on a MMSEstructure. It allows iterative computing to minimize the variance of theerror between input and output of the slicer. The slicer box, as used inFIG. 5 may or may not include error correction decoding. The sliceroutputs the estimate of the data ŝ, as well as 1/ŝ and {circumflex over(as)}. For OFDM with QAM modulation, 1/ŝ typically is found from alook-up table. Iterative software processing can also used in thereceiver of FIG. 5. The iteration method contains the following stepsfor iteration round i:

[0069] Input: observation Y₀, as well as the (i−1)-th estimate ofamplitudes â(i−1), derivatives {circumflex over (d)}(i−1), and dataŝ(i−1)

[0070] Calculation of Y₂(i), using previous estimates of derivatives{circumflex over (d)}(i−1) and data ŝ(i−1), using Y₂(i)=y−

({circumflex over (d)}(i−1)ŝ(i−1))

[0071] Newly estimate amplitudes â(i) from Y₂(i), and (not depicted)possibly exploiting knowledge of amplitudes and derivatives in theprevious frame.

[0072] Newly estimate data ŝ(i), and the corresponding values of 1/ŝ(i)(e.g. table look-up), and â(i)ŝ(i)

[0073] Calculation of Z₆(i), Z₇(i), Z₈(i), Z₉(i). Here Z₉(i) acts as(correction of) the estimate {circumflex over (d)}.

[0074] Integration of Z₉(i) over various rounds, for instance{circumflex over (d)}(i)=α{circumflex over (d)}(i−1)+(1−α)Z₉(i)

[0075] (not depicted) use knowledge of amplitudes and derivatives in theprevious frame.

[0076] Output: new estimate of amplitudes â(i), derivatives {circumflexover (d)}(i), and data ŝ(i)

[0077] Starting condition is the all-zero vector for â(0), {circumflexover (d)}(0) and ŝ(0).

[0078] One can take the filters 72 and 76 non-adaptive and identical toM₆ M₁ and M₇=M₂ of FIG. 3, respectively. A practical value for theintegration constant can be α=0.9,so {circumflex over(d)}(i)=0.9{circumflex over (d)}(i−1)+0.1Z₉(i).

[0079] It appears that several implementations refines are possible asare shown in FIG. 6. Here, the inverse of

is implemented as a Finite Impulse Response FIR filter. The secondfilter M₇ is implemented as an IIR smoothing filter. Lastly, anFFT—weighting—FFT filter is applied to create an estimate of the ICI.

[0080] Many further improvements are foreseen: Use of amplitude andderivatives of previous frames to better estimate the amplitude andderivative. This can be done either as indicated as ‘optional step’ inthe algorithms, or taking the initial condition of the iteration as anextrapolation of results from the previous OFDM frame, with â(0) for thenew frame equals â(final ) plus T {circumflex over (d)}(0), the lattercorrected from the duration of any cyclic prefix or guard interval.

[0081] The filters in the receiver, in particular M₁, M₂, M₆, M₇ may ina practical receiver be fixed or be chosen from a library of precomputedvalues. For instance, the receiver control system may upon its knowledgeof the propagation environment choose between optimized settings forstationary reception (in which most of the ICI cancellation is switchedof), slow mobile reception (some ICI cancellation), or fast mobilereception (aggressive ICI cancellation).

[0082] Furthermore, adaptive filters could be used. These can usereliability information about estimates. This can be achieved byadaptive matrices or identification of erasures in the estimates.

[0083] MC-CDMA is an extension of the basic OFDM principle. In 1993,this form of Orthogonal Multi-Carrier CDMA was proposed. Basically, itapplies OFDM-type of transmission to a multi-user synchronous DS-CDMAsignal. So it is vulnerable to Doppler. As illustrated in FIG. 7, we usethe following vector notation. For OFDM, vector s of length N carries a‘frame’ of user data, with s=[s₀, s₁, . . . s_(N−1)]^(T), where theelements s_(n) are user symbols. In MC-CDMA, s=Cx, where C is an N×Ncode matrix and x=[x₀, x₁, . . . x_(N−1)]^(T) represents a frame of userdata. We will refer to x as N user signals, without explicitlyidentifying whether or not all symbols come from the same end-user. Thek-th column of C represents the ‘spreading code’ of user data stream k,and will be denoted as (C_(k)[0], . . . c_(k)[N−1])^(T). A commonly usedspecial case, which we will also consider here, is C=N^(½)WH_(N) whereWH_(N) is the Walsh-Hadamard matrix of size N×N. In that case,C=C⁻¹=C^(H), so CC=I_(N) wherein I_(N) is the N×N unit matrix. Inanother special case, namely that of C=I_(N), the MC-CDMA system reducesto OFDM. For ease of analysis, we normalize the modulation asE[x_(i)x_(j)]*=δ_(ij), or equivalently E[xx^(H)]=I_(N). ThenE[ss^(H)]=EC[xx^(H)]C^(H)=CC^(H)=I.

[0084]FIG. 7 illustrates such a MC-CDMA transmitter. Frames are createdby a serial-to-parallel (S/P) conversion of an incoming stream of databy a serial-to-parallel converter 90, applying the code spreading by aspreader 92, an I-FFT 94 and a parallel-to-serial conversion 96 withprefix insertion. We will address the transmission of a single frame,and assume that interframe interference is avoided by choosingappropriate guard intervals. Hence, the elements of vectors s and x areconstant with time. The frame duration, excluding any guard interval isT_(s), where ω_(s)T_(s)=2π.

[0085] If the receiver architectures proposed in the previous sectionsare used for MC-CDMA, basically, the FEC is replaced by the (inverse)code matrix C. The receiver depicted in FIG. 8 is an extension of thereceiver of FIG. 5 to accommodate MC-CDMA instead of OFDM. Thedifference with the OFDM receiver resides in the box drawn with thedashed line. For OFDM this basically contains a gain control and aslicer. For MC-CDMA, we added in the code spreading matrix C (which isused in the spreaders 106 and 110 and the despreader 102). The receiveris designed such that all matrixes are fixed (or taken from a library ofpre-computed values) and that no divisions are necessary. An exceptionis the weight matrix W (used in the filter 100), which has channeladaptive settings.

[0086] It can be shown that in an MMSE setting, W only has non-zerocomponents on the diagonal, with$w_{n,m} = \frac{\delta_{n,m}a_{n}^{*}}{{a_{n}a_{n}^{*}} + {constant}}$

[0087] wherein the constant depends on the noise floor. Details of thecircuitry to estimate amplitudes are not shown in FIG. 8, but can bebased on known principles.

[0088] For MC-CDMA, the slicer bases its symbol decisions on energyreceived from all subcarriers, thus the reliability of estimates ŝ ismuch more accurate in subcarriers that are in a fade.

[0089] The principles of the receivers described above can also becombined with an FFT which handles more samples than the usual size FFT.One example is the use of a fractionally spaced FFT, another one is thedouble sized FFT. Moreover, one can even design a system that separatescomponents received via amplitudes from those received over derivatives.

[0090] Although in the above mainly an OFDM transmission system isdescribed, the invention is also and equally well applicable to othermulticarrier transmission systems such as MC-CDMA transmission systems.Large part of the receivers may be implemented by means of digitalhardware or by means of software which is executed by a digital signalprocessor or by a general purpose microprocessor.

[0091] The scope of the invention is not limited to the embodimentsexplicitly disclosed. The invention is embodied in each newcharacteristic and each combination of characteristics. Any referencesigns do not limit the scope of the claims. The word “comprising” doesnot exclude the presence of other elements or steps than those listed ina claim. Use of the word “a” or “an” preceding an element does notexclude the presence of a plurality of such elements.

1. A transmission system for transmitting a multicarrier signal from atransmitter (10) to a receiver (20), the multicarrier signal comprisinga plurality of subcarriers, the receiver (20) comprising a channelestimator (28) for estimating amplitudes of the subcarriers and forestimating time derivatives of the amplitudes, the receiver (20) furthercomprising an equalizer (24) for canceling intercarrier interferenceincluded in the received multicarrier signal in dependence on theestimated amplitudes and derivatives (29), wherein the channel estimator(28) and/or the equalizer (24) are arranged for exploiting an amplitudecorrelation between the amplitudes of different subcarriers and/or forexploiting a derivative correlation between the derivatives of differentsubcarriers.
 2. The transmission system according to claim 1, whereinthe receiver (20) is a linear receiver and wherein the channel estimator(28) comprises a reduced complexity filter for deriving vectors of theestimated amplitudes and derivatives (29) from vectors of receivedsymbols (23) and vectors of estimated symbols (27).
 3. The transmissionsystem according to claim 1, wherein the receiver (20) is a decisionfeedback receiver and wherein the channel estimator (28) comprises asmoothing filter (76) for smoothing the estimated amplitudes and/orderivatives.
 4. The transmission system according to claim 3, whereinthe receiver (20) comprises a multiplication by N×N leakage matrix

, and wherein the multiplication is implemented as a sequence of anN-point IFFT (82), N pointwise multiplications (84) and an N-point FFT(86).
 5. The transmission system according to claim 3 or 4, wherein thedecision feedback receiver comprises a decision feedback loop, andwherein the decision feedback loop comprises an error correction decoder(42).
 6. The transmission system according to any one of the precedingclaims, wherein the multicarrier signal is an OFDM signal.
 7. Thetransmission system according to any one of the claims 1 to 5, whereinthe multicarrier signal is a MC-CDMA signal.
 8. A receiver (20) forreceiving a multicarrier signal from a transmitter (10), themulticarrier signal comprising a plurality of subcarriers, the receiver(20) comprising a channel estimator (28) for estimating amplitudes ofthe subcarriers and for estimating time derivatives of the amplitudes,the receiver (20) flirter comprising an equalizer (24) for cancelingintercarrier interference included in the received multicarrier signalin dependence on the estimated amplitudes and derivatives (29), whereinthe channel estimator (28) and/or the equalizer (24) are arranged forexploiting an amplitude correlation between the amplitudes of differentsubcarriers and/or for exploiting a derivative correlation between thederivatives of different subcarriers.
 9. The receiver (20) according toclaim 8, wherein the receiver (20) is a linear receiver and wherein thechannel estimator (28) comprises a reduced complexity filter forderiving vectors of the estimated amplitudes and derivatives (29) fromvectors of received symbols (23) and vectors of estimated symbols (27).10. The receiver (20) according to claim 8, wherein the receiver (20) isa decision feedback receiver and wherein the channel estimator (28)comprises a smoothing filter (76) for smoothing the estimated amplitudesand/or derivatives.
 11. The receiver (20) according to claim 10, whereinthe receiver (20) comprises a multiplication by N×N leakage matrix

, and wherein the multiplication is implemented as a sequence of anN-point IFFT (82), N pointwise multiplications (84) and an N-point FFT(86).
 12. The receiver (20) according to claim 10 or 11, wherein thedecision feedback receiver comprises a decision feedback loop, andwherein the decision feedback loop comprises an error correction decoder(42).
 13. The receiver (20) according to any one of the claims 8 to 12,wherein the multicarrier signal is an OFDM signal.
 14. The receiver (20)according to any one of the claims 8 to 12, wherein the multicarriersignal is a MC-CDMA signal.